All Disney parks have a policy where they tell guests that they must somehow use a mobility aid if they tire easily. There are rental sites that offer rollators, wheelchairs, pushchairs, special needs strollers and
ECVs/scooters. That said you need to get the kid a wheelchair to help him not fatigue.
The GAC cannot get guests to the head of the line usually. It cannot shorten the walk and at times the line is longer for disabled guests than the regular line. I had to wait for Dumbo at
Disneyland for 3 turns so that I did not get the head of the line. WDW and DLR are similar in having at times very long disabled lines. There was at Disneyland about a 10 minute wait for pirates but I had to wait for half an hour because I used the disabled line for my
scooter.
GAC and disabled services is for a party of 5 plus the disabled guest for a total of 6 people. The GAC and disabled services are only for the guest and his group so no having granny use her GAC or wheelchair to get her family through lines faster when she is not riding.
GAC is not needed if a person is obviously disabled such as using a wheelchair or crutches. GACs can be given for hidden disabilities such as vision limits, autism, sun, and hearing even if the guest is in a wheelchair.
My recommendation is that you get the GAC for no stairs. Rent or buy a wheelchair for the kid. If he wants to walk on a short line let him but make sure it is obviously a short line. REad the FAQs for this board as there are lots of aids in them FAQs.
A. Your party splits into two groups and one group rides with the boy then goes off to rest or whatever while waiting for the rest of your group to get off the ride.
B. Your party splits into two groups and one group waits with the kid in the disabled line then when the other group is ready to board then the whole party boards together.
Use touring guides and online touring tips to minimize waits through slow times of the day, knowing which rides get long lines fast, and using fast passes. Planing is key. Knowledge is key to having a fun trip like where is the bathrooms, where to eat, and what street performances are happening.
For the frustration he needs to learn to handle things. Music players, game boys, chew toys, tid bits of food, games, and other busy stuff help people wait. In restaurants I demolish straws with my fingers. A bored mind leads to frustration so you need to keep his mind off of things he cannot control and on fun things. If he gets frustrated because he did not get picked for a show then avoid those or use psychology and other tricks to help the kid handle not being picked for a show.
Talk to CMs/cast members as they can sometimes help you in ways you would not believe.